What percentage of the students surveyed who supported both proposals A and B preferred Sunita for student union president?

Total number of students surveyed= 500

Every student prefers one of the two candidates. Ragini(R) and Sunita(S).

Thus, R+S=500.

Clue 2 says,

Among the 200 students who preferred Sunita

=> The number of students who support Sunita(S)=200

and, The number of students who supported Ragini(R)=300.

Continuing with clue 2;

Among the 200 students who preferred Sunita as student union president, 80% supported proposal A.

=> $200 * (80 / 100 ) = 160$

=> 160 students who supported Sunita also supported the proposal A.

Clue 3 says,

Among those who preferred Ragini, 30% supported proposal A.

We know, The number of students who supported Ragini(R)=300.

=> $300 * (30 / 100) = 90$

=> 90 students who supported Ragini also supported proposal A.

Clue 4 says,

20% of those who supported proposal B preferred Sunita.

We know, 250 students supported proposal B. (clue 1)

=> $250 * (20 / 100) = 50$

=> 50 students who supported Proposal B also supported Sunita.

Clue 6 says,

Every student who preferred Sunita and supported proposal B also supported proposal A.

We know, 50 students who supported Proposal B also supported Sunita

=> All those 50 students will also prefer proposal A.

=> There will be no student who prefer only Proposal B.

=> There will be $160 - 50 =110$ students who prefer proposal A only.

=> There will be $200 - 110 - 50 = 40$ students who do not prefer any of the proposal.

Clue 7 says,

Among those who preferred Ragini, 20% did not support any of the proposals.

We know, The number of students who supported Ragini(R)=300.

=> $300 * (20/100) = 60$

=> There are 60 students among those who prefer Ragini, who do not prefer any of proposal A and B

Clue 5 says,

40% of those who did not support proposal B preferred Ragini.

we know, 250 students supported proposal B.

=> $250 * (40 / 100) = 100$

=> 100 people who preferred Ragini did not support proposal B

=> these 100 people will include those who -

1. only support proposal A.

2. Do not support any of proposal A or B.

Now, we know, there are 60 students among those who prefer Ragini, who do not prefer any of proposal A and B.

=> there will be $100 - 60 = 40$ people who prefer only proposal A.

Now, we know, There are 90 people who preferred proposal A for Ragini.

And, 40 people who preferred only proposal A

=> $90 - 40 = 50 people will support both A and B.

=> there will be $200 - 50 = 150$ people who preferred only proposal B.

Students who supported both proposals $=50+50=100$

$\therefore \text { required \%age }=\frac{50}{100} \times 100=50 \%$